It is possible to deploy the trained UWMMSE in a distributed fashion as the allocated power at a given node \(i\)  can be computed without explicit knowledge of the states of channels that do not include transmitter \(i\)  or receiver \(r(i)\) .
However, similar to WMMSE [1]}, we need to make some key assumptions regarding the information available to each transceiver pair.
Primarily, each transmitter \(i\)  should have estimates of the local channel state \(h_{ji}\)  for all receivers \(r(j)\) .
Additionally, there should be a feedback mechanism through which receiver \(r(i)\)  can transmit information to all transmitters in the network.
Under these assumptions, each receiver \(r(i)\)  can compute its individual \(u_i^{(k)}\)  and \(w_i^{(k)}\)  and pass them on to the transmitters to compute \(v_i^{(k)}\)  for all \(k\)  unrolling layers in all nodes.
Each node is also assumed to have access to the full set of trainable weights of both GCN-based learning modules in each unrolling layer \(k\) . It is important to note here that our proposed method cannot be trained in a distributed fashion as the used formulation of GCN [2]} requires access to the entire CSI matrix and thus necessitates centralized training. But once trained, it is sufficient to have the indexed row and column available for computing the output of any given node, allowing distributed implementation of the trained model. Such a setup would still incur additional communication overheads and the rate of power allocation would be limited by the speed of the feedback link between a given transceiver pair.
